I just checked the Lichess board editor tool and it won’t let you continue analyzing with an engine if you have an illegal board setup (like the two kings adjacent to each other).

I haven’t tried this yet, but I think you can set up and analyze board positions that are legal but that could never be reached in a real game (e.g, having nine pawns of one color).

Oh, I was thinking board positions that could never be reached in a real game. Actually, I have no idea what the technical definition of a legal board state is, haha.